====== Model ======

  - will create the simplest possible model to study this question
  - single-locus haploid replicators for both genes and memes.  Individuals are hosts to each
  - just two alleles for each replicator: C & D
  - interaction/game between replicators in each host, payoff determines their fitness
  - memetic replication horizontal, genetic vertical.  Two variants to consider: memes inherited with genes or not
  - rank ordering of payoffs important.  16 asymmetric games
    - assume CC > DD for both replicators
    - without loss of generality define CC payoff = 1 for both, and DD = 0 for both
    - four remaining payoff parameters
    - structured population

====== Details ======

Payoff matrix:
|      |     ^               Gene             ^^
|      |     ^        C        ^       D       ^
^ Meme ^  C  |      1, 1       |  $S$, $\tau$  |
^ :::  ^  D  |  $T$, $\sigma$  |  0, 0         |

Possible games((N=Nash equilibrium)):
|        |       ^                                                        Gene                                                         ^^^^
|        |       ^  ←\\ ←\\ $\tau<1, \sigma>0$  ^  ←\\ →\\ $\tau<1, \sigma<0$  ^  →\\ ←\\ $\tau>1, \sigma>0$  ^  →\\ →\\ $\tau>1, \sigma<0$  ^
^  Meme  ^  ↑ ↑\\ $T<1\\ S>0$  |  Harmony\\ N .\\ . .  |              N .\\ . .               |       . N\\ . .       |            . N\\ . .            |
^  :::   ^  ↑ ↓\\ $T<1\\ S<0$  |       N .\\ . .       |  Coordination/Stag-hunt\\ N .\\ . N  |       . .\\ . .       |            . .\\ . N            |
^  :::   ^  ↓ ↑\\ $T>1\\ S>0$  |       . .\\ N .       |              . .\\ . .               |  Chicken\\ . N\\ N .  |            . N\\ . .            |
^  :::   ^  ↓ ↓\\ $T>1\\ S<0$  |       . .\\ N .       |              . .\\ . N               |       . .\\ N .       |  Prisoners Dilemma\\ . .\\ . N  |


Dynamics:
  * birth-death process
  * birthrate contains selection
  * deathrate just ecological
  * births: I + J --> 2 I + J @ rate Pij
  * deaths: 3 N --> 2 N
  * expect should give replicator equation in limit of large, well-mixed popn (up to a time rescaling)
